
where the coefficient \(C_s^{i_s}\)  (\(s=1,\cdots ,d_0+1\) ) is a rational function of external momenta, and \(I_s^{i_s}\)  is the \(s\) -gon scalar integral. If \(d_0=4\) , then the corresponding master integrals are traditionally referred as tadpole, bubble, triangle, box and pentagon integrals (the tadpole integrals vanish if the corresponding propagators are massless).
So the task of computing an one-loop amplitude is reduced to determining the coefficients of these master integrals.
These coefficients can be derived by either integrand reduction [1]} algebraically, or the unitarity method [2]}, [3]}, [4]}.
The idea underlying the unitarity method is to constrain amplitudes by their branch cuts, more explicitly, comparing two sides of (REF ) after cutting several propagators.
By using the usual unitarity cuts (cut two propagators corresponding to a physical channel), the explicitly analytical expressions of these coefficients have been given in [5]}, [6]}, [7]}.
However, the analytic results of the tadpole coefficients are missing.
